Kevin is 32 years older than Luis. Fourteen years ago, Kevin was 5 times as old as Luis. How old is Luis now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Luis. Let Kevin's current age be $k$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $k = l + 32$ Fourteen years ago, Kevin was $k - 14$ years old, and Luis was $l - 14$ years old. The information in the second sentence can be expressed in the following equation: $k - 14 = 5(l - 14)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = l + 32$ . Substituting this into our second equation, we get the equation: $(l + 32)$ $-$ $14 = 5(l - 14)$ which combines the information about $l$ from both of our original equations. Simplifying both sides of this equation, we get: $l + 18 = 5 l - 70$ Solving for $l$ , we get: $4 l = 88$ $l = 22$.